# How do you solve 9(16)^(2x)=589824?

Sep 13, 2016

$x = 2$

#### Explanation:

Start off by dividing both sides of the equation by $9$

${\left(16\right)}^{2 x} = 65536$

Now we can rewrite in terms of base $2$

${\left({2}^{4}\right)}^{2 x} = {2}^{16}$

Using rules of exponents we can write

${2}^{8 x} = {2}^{16}$

Since both sides of the equation are written in terms of the same base we can write

$8 x = 16$

Dividing both sides by $8$ we get

$x = 2$